Algebra Commons^™

Rockin’ Rover On The Rainbow Road, Michael Kolta, Lawrence Burgee, Ying Yuan

Transformations

This paper presents a progressive series of age-appropriate lesson plans for grades K-12 that all use the same interdisciplinary activity to educate students about Science, Technology, Engineering, Art, and Mathematics (STEAM) simultaneously. Technology from Texas Instruments (TI) was employed including a TI Nspire graphing calculator that can run Python programs, a TI Innovator Hub, and a TI Rover. The TI Rover is a small, robotic car that has sensors and is controlled by the calculator via the Hub hardware interface. A Python program was developed that uses the color sensor in the Rover to detect the color on colored paper …

Trattato Dell’Alcibra Amuchabile (Anonimo): A Guided Translation, Gary Towsley, Olympia Nicodemi

Geneseo Authors

The Trattato dell’Alcibra Amuchabile is a pre-modern algebra text from c. 1365. It is written in a Tuscan dialect of Italian and is situated in the abbacus school tradition, schools that taught the mathematics needed for a mercantile society. Like all the algebra written in Italy at the time, it was inherited from al-Khwarizmi and, like his, written with no symbols—no x’s, y’s, plus signs, etc. It was what is sometimes called “rhetorical algebra.”  There is very little source  material available in English from this important era in the history of algebra. This book helps fill that gap. …

Course Portfolio: Elements Of Physics Phys 151, Evan A. Rich

UNL Faculty Course Portfolios

This course portfolio documents the instructional design, teaching methods, and ongoing assessment efforts for PHYS 151: Elements of Physics, an algebra-based introductory physics course at the University of Nebraska-Lincoln. The course serves a broad undergraduate population, including architecture, construction management, and life science majors. The portfolio describes the teaching framework that integrates pre-lecture video preparation, active in-class engagement through iClicker questions, and collaborative weekly recitation sections, all unified around a structured six-step problem-solving approach. A central concern of the course is building students’ self-efficacy in physics, particularly among those with math anxiety or limited preparation. Two assessments are reported: a …

Fostering A Growth Mindset In Mathematics: Faculty And Student Experiences, Yolanda G. Rush

Theses and Dissertations

According to the Center for Community College Student Engagement (2019), many students attending two-year institutions need productive persistence strategies, including the development of a growth mindset. Although some growth mindset interventions have been effective in improving academic achievement among students (Boaler, 2016; Canning et al., 2024) and persistence (Lewis, 2019) among students, especially those with developmental needs (Suh et al., 2019) and those in mathematics, little is known about the experiences of students and teachers (i.e., students’ perceptions of teachers’ intentions and implementation) as teachers work to foster a growth mindset culture (Murphy et al., 2021). In this dissertation, I …

Test Retakes In Introductory Math Courses, John Hird, Chris Mcclain

2026 Scholarly Teaching Conference: Poster Session Papers

In this poster, we describe the implementation of an exam retake model using specifications grading for math courses taken by non-STEM majors. This system was implemented by two faculty members over three years in two sequential courses. During that time, we tried several versions of allowed retakes, with varying restrictions on partial credit. Some of the challenges that we faced were scaling the system for use by different faculty members and with different courses, managing faculty workload on writing and grading multiple exams, and managing student expectations.

Algebraic Topics For Future Middle School Teachers, Leonard Van Wyk

Department of Mathematics and Statistics - Faculty Scholarship

This text contains algebraic concepts relevant to the middle school mathematics curriculum. Topics include the basics of number theory, functions, linear systems, matrices, and polynomials.

Number Talks To Promote Discourse In The Algebra 1 Classroom: A Number Talk Curriculum Development For A Unit On Quadratic Expressions, Lindsay C. Borger

Masters Theses/Capstone Projects

This project sought to develop a curriculum of Number Talks for use at the secondary level, specifically in an Algebra 1 class as a supplement to a unit on quadratic expressions. The project begins with a look at existing research on constructivism and social constructionism as well as the reforms in mathematics education informed by those learning theories. It then looks at calls for more discourse in the mathematics classroom as a part of these reform efforts, and the part Number Talks play in fostering discourse and mathematical thinking for students. The Number Talk curriculum includes a guide for implementing …

A Comparative Analysis Of Early Algebraic Thinking Activities From U.S. And Singapore Primary Textbooks, Christian Joel Hernandez

Theses and Dissertations

Many studies highlight the challenges students face when transitioning to algebra at the secondary level. Introducing algebraic concepts and fostering algebraic thinking at the primary level can help mitigate these difficulties. Prior to formal algebra instruction, early algebra can be cultivated as a mode of thinking known as algebraic thinking. Several international curricula, such as Singapore Math, incorporate early algebraic thinking into the early stages of schooling. Singapore Math, renowned for its high performance in international assessments, has been widely adopted by schools seeking to replicate its success.

This study compares two primary-level mathematics curricula—CCSSM-aligned textbooks and Singapore Math—specifically focusing …

A Comparison Of Assessment Experiences Between Standards-Based Practices And Traditional Practices Within Secondary Mathematics Classrooms, Emily Mayes

Honors Theses

The purpose of this research was to compare assessment experiences and find ways to improve those experiences for students in two mathematics classrooms: one classroom that employs Standards-Based Grading and one classroom that uses traditional grading practices. The research examines students’ perceptions regarding their level of preparation, their anxiety levels surrounding assessment, the validity of assessments, and using assessments and grading practices to give accurate indications of student progress in their learning, given the students’ perceptions. Students in both settings voluntarily and anonymously participated in completing pre- and post-assessment free-response surveys which asked questions about students’ assessment experiences. This research …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

An Introduction To The Algebra Revolution, Art Bardige

Numeracy

Bardige, Art. 2022. The Algebra Revolution: How Spreadsheets Eliminate Algebra 1 to Transform Education; (Bookbaby) 135 pp. UNSPSC 55111505.

The Algebra Revolution: How Spreadsheets Eliminate Algebra 1 to Transform Education argues that Algebra 1 can be eliminated by teaching mathematics through spreadsheets. Such a change would eliminate the greatest roadblock to student achievement.

Understanding And Advancing College Students' Mathematical Reasoning Using Collaborative Argumentation, Rachel Kay Heili

Graduate Theses/Dissertations

This study explored students’ mathematical reasoning skills and offered supports to advance them through a collaborative argumentation framework in a college intermediate algebra class. The goals of this study were to make observations about student reasoning, identify specific actions to address those observations, and document student growth in reasoning as a result of those actions. An iterative analysis, mixed method study was conducted in which the researcher engaged students in responding to questions that required conceptual understandings using a collaborative argumentation framework as a tool to identify and code components of their responses—claim, evidence, and reasoning. After coding and analyzing …

Interactive White Boards In A Secondary Mathematics Classroom, Leann Bolhuis

Mathematics Graduate Theses

"A Formal Portfolio Submitted to the Faculty of the DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE In Partial Fulfillment of the Requirements For the Degree of MASTER OF SCIENCE IN MATHEMATICS".

Bbt Acoustic Alternative Top Bracing Cadd Data Set-Norev-2022jun28, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set consists of an overview presentation (PDF-formatted) file and companion video (MP4) and CADD files (DWG & DXF) for laser cutting the ETSU-developed alternate top bracing designs and marking templates for the STEM Guitar Project’s BBT (OM-sized) standard acoustic guitar kit. The three (3) alternative BBT top bracing designs in this release are
(a) a one-piece base for the standard kit's (Martin-style) bracing,
(b) 277 Ladder-style bracing, and
(c) an X-braced fan-style bracing similar to traditional European or so-called 'classical' acoustic guitars.

The CADD data set for each of the three (3) top bracing designs includes …

Bbt Side Mold Assy, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set covers the design and fabrication information of the ETSU Guitar Building Project’s BBT (OM-sized) Side Mold Assy for use with the STEM Guitar Project’s standard acoustic guitar kit. The extended 'as built' data set contains an overview file and companion video, the 'parent' CADD drawing, CADD data for laser etching and cutting a drill &/or layout template, CADD drawings in AutoCAD .DWG and .DXF R12 formats of the centerline tool paths for creating the mold assembly pieces on an AXYZ CNC router, and support documentation for CAM applications including router bit specifications, feeds, speed, multi-pass …

Interdisciplinary Thinking: Financial Literacy Crosses Disciplinary Boundaries, Marla A. Sole

Publications and Research

Financial literacy is ideally suited to be integrated into mathematics courses and taught in an interdisciplinary manner. Students learn best and are motivated when tackling real-world meaningful questions. This article shares how elementary mathematics was applied to better understand the debate about raising the minimum wage and the United States National Debt. To serve as a guide for other teachers who wish to incorporate financial literacy into their mathematics courses and take an interdisciplinary approach, this article suggests readings, data sets, and pedagogical practices. Students were engaged and enthusiastic to work on problems that challenged their thinking about financial issues.

Proctoring And Apps In College Algebra, Cynthia M. Shelton

Theses and Dissertations--Education Sciences

The pandemic forced more instructors and students to move to online learning. For the first time, many experienced a loosening of the reigns and were forced to allow students to submit non-proctored work. Many may have questioned what students really learned in the year 2020. Many college math course competencies emphasize procedures. Now that apps can do that for students, where does that leave math instructors? Additionally, online instruction has exploded over the last decade and has challenged the teaching of college mathematics. While online instruction opens the door to access, it does beg the question of whether students complete …

Combining Transformation Of Graphs With Solutions To Absolute Value Inequalities, Ryan D. Fox

Colorado Mathematics Teacher

I present how transformations can be applied to support students’ solving linear inequalities involving absolute value. In particular, the horizontal dilations/compressions and translations of graphical representations of distances from zero along a number line are important tools to emphasize a visual representation of the solutions to absolute value inequalities.

Pemahaman Ungkapan Algebra Dalam Kalangan Murid Tingkatan Dua, Hamid Azizah

Student Works (2020-2029)

Pemahaman tentang konsep ungkapan algebra penting bagi murid sekolah menengah kerana ia merupakan asas kepada pembelajaran matematik di peringkat menengah dan peringkat pengajian tinggi memandangkan kesukaran dalam pembelajaran algebra menjadi semakin kritikal. Kajian ini adalah untuk mengenal pasti pemahaman murid Tingkatan Dua tentang ungkapan algebra dengan berlandaskan konstruktivisme radikal. Penyelidikan ini menggunakan kajian kes sebagai reka bentuk kajian, yang membabitkan data berbentuk kualitatif. Peserta kajian membabitkan enam murid dari tiga kategori pencapaian akademik dengan menggunakan teknik persampelan bertujuan. Data kajian terkumpul melalui tiga sesi temu duga klinikal dengan menggunakan perakam video, catatan murid dan pengkaji. Data kajian dianalisis dengan menggunakan …

Evolution Of Computational Thinking Contextualized In A Teacher-Student Collaborative Learning Environment., John Arthur Underwood

LSU Doctoral Dissertations

The discussion of Computational Thinking as a pedagogical concept is now essential as it has found itself integrated into the core science disciplines with its inclusion in all of the Next Generation Science Standards (NGSS, 2018). The need for a practical and functional definition for teacher practitioners is a driving point for many recent research endeavors. Across the United States school systems are currently seeking new methods for expanding their students’ ability to analytically think and to employee real-world problem-solving strategies (Hopson, Simms, and Knezek, 2001). The need for STEM trained individuals crosses both the vocational certified and college degreed …

The Wright Stuff: An Integrative Approach To Stained Glass, Cassandra Wissink Armstrong

Professional Learning Day

In this session we'll explore the scientific and mathematical influences behind the artistic stained glass creations of Frank Lloyd Wright, and use them to create our own Wright-inspired stained glass designs. This is a truly integrative lesson that touches on properties of glass, linear functions, and artistic design.

How To Calculate Pi: Buffon's Needle (Non-Calculus Version), Dominic Klyve

Pre-calculus and Trigonometry

No abstract provided.

Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg

Number Theory

No abstract provided.

Does Teaching The History Of Mathematics In High School Aid In Student Understanding?, Anne Campbell

Undergraduate Honors Thesis Projects

This research will study the effect teaching the history of mathematics in a high school classroom has on student understanding. To accomplish this, lessons both including and excluding historical background on different topics were taught in an Honors Algebra 2 class in the high school setting. This research aims to engage student learning and investigation of topics that normally do not draw a lot of student focus and spark a new or revived interest in mathematics for students by broadening lessons to include material of which students would not otherwise be exposed. The lessons themselves aim to engage other current …

Otto Holder's Formal Christening Of The Quotient Group Concept, Janet Heine Barnett

Abstract Algebra

No abstract provided.

The Effects Of Motivation, Technology And Satisfaction On Student Achievement In Face-To-Face And Online College Algebra Classes, Hanan Jamal Amro, Marie-Anne Mundy, Lori Kupczynski

TxDLA Journal of Digital Learning

Demand for online learning has increased in recent years due to the convenience of class delivery. However, some students appear to have difficulties with online education resulting in lack of completion. The study utilized a quantitative approach with archival data and survey design. The factors of demographics, motivation, technology, and satisfaction were compared for face-to-face and online students. MANCOVA tests were performed to analyze the data while controlling age and gender to uncover significant differences between the two groups. The sample and population for this study were predominantly Hispanic students.

Motivation and Technology were non-significant, but satisfaction was proven to …

Determining The Determinant, Danny Otero

Linear Algebra

No abstract provided.

Supporting English Language Learners Inside The Mathematics Classroom: One Teacher’S Unique Perspective Working With Students During Their First Years In America, Amy Marie Fendrick

Research and Evaluation in Education, Technology, Art, and Design

Reflecting upon my personal experiences teaching mathematics to English Language Learners (ELL) in a public high school in Lincoln, Nebraska, this essay largely focuses on the time I spent as the only Accelerated Math teacher in my school building. From 2012 – 2017, I taught three different subjects at this high school: Advanced Algebra, Algebra, and Accelerated Math. This essay highlights why I chose to become a math and ELL teacher, as well as the challenges, issues, struggles, and successes I experienced during my time teaching. I focus on the challenges I faced teaching students who did not share my …

The Roots Of Early Group Theory In The Works Of Lagrange, Janet Heine Barnett

Abstract Algebra

No abstract provided.

Solving A System Of Linear Equations Using Ancient Chinese Methods, Mary Flagg

Linear Algebra

No abstract provided.